Attempt the implementation of missing reinit! for dual cache

[j-fu]

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

This is an attempt to implement the missing reinit! metod for the dual cache.
I am however unsure if this is correct, at least the test works.